Concessive clauses in Spanish are introduced by conjunctions like aunque, por más que... or pese a que...These clauses introduce some kind of objection or difficulty in relation to the main clause, however they don't interfere with the fulfilment of the action in the main clause.
Here are some examples:
"Aunque no soy muy aficionado al fútbol, ayer vi el partido en la tele."
(Although I am not very enthusiastic about fooball, I watched the match on the telly yesterday.)
"A pesar de no tener un salario alto María tiene una casa lujosa y dos coches."
(Despite not having a high salary María has a luxurious house and two cars.)
"Pese a que el hombre confesó su crimen, el juez le dio una condena muy dura."
(Even though the man confessed his crime, the judge gave him a very hard sentence.)